Question

Determine the ratio in which y-x+2=0 divides the line joining (3,-1) and (8,9)

Answer 1

let t line x-y-2=0 divid t line segment in t ratio k : 1 at point C

so coordinates of C are

{ ( 8k +3 / k+1) , ( 9k-1 / k+1 ) }

C lies on x - y - 2 = o

so, subs coordinates of x,y in tis eq.

( 8k +3 / k+1) - ( 9k-1 / k+1 ) - 2 = 0

8k +3 - 9k +1 - 2k -2 / k+1 = 0

- 3k +2 / k+1 = 0

-3k + 2 = 0

=> k = 2/3

i.e. 2 : 3